The present invention relates to a method of polarimetry for use in the identification, examination on purity, determination of the concentration and the like of a solute in a liquid specimen, and a method of urinalysis using the same.
A polarimeter is employed as an optical rotation detecting type saccharimeter for detecting the concentrations of fructose, sucrose, glucose, and the like contained in an aqueous solution. It can also determine especially the concentrations of optical active substances such as glucose and protein in a urine. Therefore, it is expected to come into wide use as a urinalysis equipment which requires no consumable articles such as test papers.
FIG. 6 shows a conceptual constitution of one example of conventional polarimeters. The polarimeter is for determining the magnitude of spontaneous optical rotatory power, i.e., an angle of rotation attributed to a spontaneous optical rotatory power of a spontaneous optical active substance in a specimen to be detected. In concrete, the angle of spontaneous optical rotation is determined based on an angle of magnetorotation (compensated value) by an optical Faraday effect when the spontaneous optical rotation attributed to the spontaneous optical active substance is canceled (compensated) by the magnetorotation.
A semiconductor laser module 21 configured with a sodium lamp, a band-pass filter, a lens, a slit, and the like projects a substantially parallel light composed of a sodium D ray having a wavelength of 589 nm. A polarizer 23 transmits only a component that has a specific plane of vibration out of the light projected from the semiconductor laser module 21. A sample cell 25 for holding a specimen to be detected has a pair of mutually opposing transparent transmission surfaces, and is arranged so that the light projected from the semiconductor laser module 21 can transmit through the inside thereof. An analyzer 26 transmits only a component that has another specific plane of vibration out of the light transmitted through the sample cell 25. The relative angle "THgr" formed between the transmission axis of the polarizer 23 and the transmission axis of the analyzer 26 is fixed at xcfx80/2. A photosensor 27 detects the component transmitted through the analyzer 26 out of the light projected from the semiconductor laser module 21. A Faraday cell 24 modulates and controls the plane of vibration of the light projected from the semiconductor laser module 21 based on a modulation signal outputted from a signal generator 30 and a control signal outputted from a computer 22. The Faraday cell 24 is driven by a Faraday cell driver 29. A lock-in amplifier 28 performs a phase sensitive detection on the output signal from the photosensor 27 by using the modulation signal outputted from the signal generator 30 as a reference signal. The computer 22 calculates the angle of rotation attributed to the specimen to be detected accommodated in the sample cell 25 based on the control signal, and the output signal from the lock-in amplifier 28.
As described above, by sweeping the angle of the plane of vibration by the Faraday cell, it becomes possible to achieve simplification and compactness thereof as compared with apparatuses using other means for modulating the plane of vibration.
Below, the principle of the conventional polarimeter will be described.
The Faraday cell 24 modulates the plane of vibration of the light projected from the semiconductor laser module 21 and transmitted through the polarizer 23 with an amplitude of xe2x80x9cxcex4xe2x80x9d and an angular frequency of xe2x80x9cxcfx89xe2x80x9d. In this step, the intensity xe2x80x9cIxe2x80x9d of the light that has reached the photosensor 27 is represented by the following equation (1):
I=Txc3x97I0xc3x97{cos["THgr"xe2x88x92xcex1+xcex2+xcex4xc3x97sin(xcfx89xc3x97t)]}2xe2x80x83xe2x80x83(1)
where T: transmittance of the specimen,
I0: intensity of the light incident upon the specimen,
"THgr": relative angle formed between the transmission axis of the polarizer 23 and the transmission axis of the analyzer 26,
xcex1: angle of rotation attributed to the specimen,
xcex2: angle of rotation of light due to the Faraday cell 24, and
t: time.
It is noted that the transmission loss and the reference loss of the sample cell 25 and the analyzer 26 respectively are ignored.
Since the relative angle "THgr" between the transmission axis of the polarizer 23 and the transmission axis of the analyzer 26 is xcfx80/2, the following equation (2) is given from the equation (1).
I=Txc3x97I0xc3x97{sin[xcex2xe2x88x92xcex1+xcex4xc3x97sin (xcfx89xc3x97t)]}2xe2x80x83xe2x80x83(2)
In case of xcex2xe2x88x92xcex1=0, in other words, when it is assumed that the angle of rotation attributed to the specimen is canceled (compensated) by the angle of rotation due to the Faraday cell 24, the equation (2) is expressed as the following equation (3):                                                         I              =                              xe2x80x83                            ⁢                                                (                                      1                    /                    2                                    )                                xc3x97                T                xc3x97                                  I                  0                                xc3x97                                  {                                      1                    -                                          cos                      ⁡                                              [                                                  2                          xc3x97                          δ                          xc3x97                                                      sin                            ⁡                                                          (                                                              ω                                xc3x97                                t                                                            )                                                                                                      ]                                                                              }                                                                                                        =                              xe2x80x83                            ⁢                                                (                                      1                    /                    2                                    )                                xc3x97                T                xc3x97                                  I                  0                                xc3x97                                  {                                      1                    -                                          [                                                                                                    J                            0                                                    ⁡                                                      (                                                          2                              xc3x97                              δ                                                        )                                                                          +                                                                                                                                                                                                      xe2x80x83                                ⁢                                                      2                    xc3x97                                                                  J                        2                                            ⁡                                              (                                                  2                          xc3x97                          δ                                                )                                                              xc3x97                                          cos                      ⁡                                              (                                                  2                          xc3x97                          ω                          xc3x97                          t                                                )                                                                              +                  …                                ⁢                                  xe2x80x83                                ]                            }                                                          (        3        )            
where Jn(X) is an nth-degree Bessel function.
The equation (3) indicates that the intensity xe2x80x9cIxe2x80x9d of the light detected by the photosensor 27 does not contain the frequency component xcfx89 of the modulation signal alone.
When it is assumed that the angle of rotation attributed to the specimen and the amplitude of the modulation are small, that is, |xcex2xe2x88x92xcex1| less than  less than 1, and xcex4 less than  less than 1, the equation (3) is approximated to the following equation (4):                                                         I              ≅                              xe2x80x83                            ⁢                              T                xc3x97                                  I                  0                                xc3x97                                                      (                                          β                      -                      α                      +                                              δ                        xc3x97                                                  sin                          ⁡                                                      (                                                          ω                              xc3x97                              t                                                        )                                                                                                                )                                    2                                                                                                        =                              xe2x80x83                            ⁢                              T                xc3x97                                  I                  0                                xc3x97                                  {                                                                                    (                                                  β                          -                          α                                                )                                            2                                        +                                          2                      ⁢                                              (                                                  β                          -                          α                                                )                                            xc3x97                      δ                      xc3x97                                              sin                        ⁡                                                  (                                                      ω                            xc3x97                            t                                                    )                                                                                      +                                                                                                                                          xe2x80x83                            ⁢                                                [                                      δ                    xc3x97                                          sin                      ⁡                                              (                                                  ω                          xc3x97                          t                                                )                                                                              ]                                ⁢                                  P                  2                                            }                                                                          =                              xe2x80x83                            ⁢                              T                xc3x97                                  I                  0                                xc3x97                                  {                                                                                    (                                                  β                          -                          α                                                )                                            2                                        +                                          2                      ⁢                                              (                                                  β                          -                          α                                                )                                            xc3x97                      δ                      xc3x97                                              sin                        ⁡                                                  (                                                      ω                            xc3x97                            t                                                    )                                                                                      +                                                                                                                                          xe2x80x83                            ⁢                              [                                                                            δ                      2                                        /                    2                                    xc3x97                                      {                                          [                                              1                        -                                                  cos                          ⁡                                                      (                                                          2                              xc3x97                              ω                              xc3x97                              t                                                        )                                                                                              ]                                        }                                                  ]                                                                        (        4        )            
This indicates that the output signal xe2x80x9cIxe2x80x9d from the photosensor 27 contains components with angular frequencies of 0 (DC), xe2x80x9cxcfx89xe2x80x9d, and xe2x80x9c2xc3x97xcfx89xe2x80x9d, respectively. By the phase sensitive detection of the value xe2x80x9cIxe2x80x9d using the modulation signal as a reference signal in the lock-in amplifier 28, it is possible to pick up the component of the angular frequency xe2x80x9cxcfx89xe2x80x9d, i.e., the signal xe2x80x9cSxe2x80x9d shown by the following equation (5):
S=Txc3x97I0xc3x972xc3x97(xcex2xe2x88x92xcex1)xc3x97xcex4xe2x80x83xe2x80x83(5)
This signal xe2x80x9cSxe2x80x9d equals zero only when xcex2=xcex1. This point is the extinction point. In the process of rotating the plane of vibration of light by the Faraday cell 24, in other words, sweeping xe2x80x9cxcex2xe2x80x9d, the value of xe2x80x9cxcex2xe2x80x9d when xe2x80x9cSxe2x80x9d becomes zero corresponds to the angle xe2x80x9cxcex1xe2x80x9d of rotation. The same is also true for the case where this process is considered based on the equation (3). Namely, upon the phase sensitive detection of the value xe2x80x9cIxe2x80x9d, the output xe2x80x9cIxe2x80x9d from the photosensor 27 becomes zero when xcex2=xcex1.
As described above, by modulating the angle of plane of vibration of light, it is possible to pick up only the signal xe2x80x9cSxe2x80x9d of the modulated frequency component selectively while separating the signal from noises attributed to an intensity of the light source, a fluctuation in the power source, a radiation and the like, thereby deriving a signal with a high S/N ratio. Therefore, the extinction point can be determined accurately by using this value of the signal xe2x80x9cSxe2x80x9d, and hence the angle xe2x80x9cxcex1xe2x80x9d of rotation can be determined with high accuracy.
However, in the above-described polarimetry, it is required to detect the output signal from the lock-in amplifier 28 while continuously changing xcex2 at a minute angular velocity so that the signal xe2x80x9cSxe2x80x9d becomes zero. For this reason, a large number of measurement points are required, and a longer duration of time is also required even by automation. Further, when the feedback control is conducted based on the measured value at each measurement point, the presence of bubbles, particles, and the like on the optical path for the light transmitted through the inside of the sample cell 25 entails fluctuations of the measured value. Therefore, an appropriate loop cannot be constructed, and hence a still longer measuring duration of time is required.
It is therefore an object of the present invention to provide a method of polarimetry and a method of urinalysis capable of solving the above-mentioned conventional problems and eliminating the influences exerted by the noises mixed due to bubbles, particles, and the like, and permitting a stable and highly accurate measurement in a short duration of time.
Apparent from the above equation (5), the relation between the intensity of the component with an angular frequency of xcfx89 and the relative angle formed between the transmission axis of the polarizer and the transmission axis of the analyzer is expressed by a linear function in the vicinity of the extinction point. In the present invention, by using this principle, the extinction point is determined from a linear regression formula (regression line) derived from the mutually different three or more relative angles and the intensities of the components whose angular frequencies are xcfx89 at respective relative angles.
Specifically, the present invention provides, as a first embodiment, a method of polarimetry for allowing a light to be incident upon a specimen to be detected containing a spontaneous optical active substance, and determining an optical rotation attributed to the spontaneous optical active substance when the light transmits through the specimen, comprising the steps of:
(a) allowing a polarized light having a known plane of vibration to be incident upon the specimen while micro-vibrating the plane of vibration by a modulation signal with an angular frequency of xcfx89;
(b) detecting a component having a specific plane of vibration out of the polarized light transmitted through the specimen by a photosensor;
(c) extracting a component with an angular frequency of xcfx89 out of an output signal from the photosensor by phase sensitive detection using the modulation signal as a reference signal; and
(d) calculating an angle of rotation attributed to the specimen based on 3 or more groups of data including a relative angle formed between a plane of vibration of the light incident upon the specimen and the specific plane of vibration of the light detected by the photosensor, and an intensity of the component with an angular frequency of xcfx89 obtained at the relative angle.
In the step (a), it is effective that the relative angle is varied by continuously rotating the plane of vibration of the polarized light incident upon the specimen.
Further, in the step (a), it is also effective that the relative angle is varied by discretely changing the plane of vibration of the polarized light incident upon the specimen.
In the step (d), it is effective that a linear regression formula is formed based on the data by using the relative angle as a criterion variable and using the intensity of the component with an angular frequency of xcfx89 as a dependent variable, and the angle of rotation attributed to the specimen is calculated based on the obtained regression formula.
Further, in the step (a), it is also effective that the relative angle is varied by rotating the plane of vibration of the polarized light incident upon the specimen by an optical Faraday effect.
Still further, in the step (d), it is effective that a linear regression formula is formed based on the data by using a magnitude of a magnetic field for obtaining the relative angle or a current amount for generating the magnetic field as a criterion variable and using the intensity of the component with an angular frequency of xcfx89 as a dependent variable, and the angle of rotation attributed to the specimen is calculated based on the obtained regression formula.
Further, the present invention also provides, as a second embodiment, a method of polarimetry for allowing a light to be incident upon a specimen to be detected containing a spontaneous optical active substance and a magneto-optical active substance, and applying a magnetic field to the specimen, thereby rotating a plane of vibration of the light transmitting though the specimen by an optical Faraday effect, and determining an optical rotation due to the spontaneous optical active substance when the light transmits through the specimen based on the magnitude of rotation of the light caused by the application of the magnetic field, comprising the steps of:
(a) allowing a polarized light having a known plane of vibration to be incident upon the specimen while micro-vibrating the plane of vibration by a modulation signal with an angular frequency of xcfx89;
(b) detecting a component having a specific plane of vibration out of the polarized light transmitted through the specimen by a photosensor;
(c) extracting a component with an angular frequency of xcfx89 out of an output signal from the photosensor by phase sensitive detection using the modulation signal as a reference signal; and
(dxe2x80x2) calculating an angle of rotation attributed to the specimen based on 3 or more groups of data including a magnitude of the magnetic field and an intensity of the component with an angular frequency of xcfx89 obtained at the magnitude of the magnetic field.
In the step (a), it is effective that the plane of vibration of the light is continuously rotated by the optical Faraday effect.
Further, in the step (a), it is also effective that the plane of vibration of the light is discretely changed by the optical Faraday effect.
Further, in the step (dxe2x80x2), it is effective that, a linear regression formula is formed based on the data, by using the magnitude of the magnetic field or the current amount for generating the magnetic field as a criterion variable and using the intensity of the component with an angular frequency of xcfx89 as a dependent variable, and that an angle of rotation attributed to the specimen is calculated based on the regression formula obtained.
Further, in the method of polarimetry, it is effective that the regression formula is calculated by using a least squares method.
Furthermore, it is effective to further comprise a step of estimating the measurement to be effective when a reliability of the regression formula is higher than a predetermined value.
At this step, it is effective to use a sum of squares of residuals xe2x80x9cSExe2x80x9d (equation (6)), a value xe2x80x9cDxe2x80x9d (equation (8)) obtained by dividing the sum of squares of residuals xe2x80x9cSExe2x80x9d by the sum of squares of the intensity values of the component with an angular frequency of xcfx89, which is obtained by substituting the data corresponding to the criterion variable of the regression formula, or a correlation coefficient xe2x80x9cRxe2x80x9d (equation (7)) expressed as each of the following formulae.                               S          E                =                              ∑                          i              =              1                        n                    ⁢                      xe2x80x83                    ⁢                                    {                                                Y                  i                                -                                  (                                      a                    +                                          bX                      i                                                        )                                            }                        2                                              (        6        )                                R        =                                            ∑                              i                =                1                            n                        ⁢                          xe2x80x83                        ⁢                          [                                                (                                                            X                      i                                        -                                          X                      _                                                        )                                xc3x97                                  (                                                            Y                      i                                        -                                          Y                      _                                                        )                                            ]                                                                          ∑                                  i                  =                  1                                n                            ⁢                              xe2x80x83                            ⁢                                                                    (                                                                  X                        i                                            -                                              X                        _                                                              )                                    2                                xc3x97                                                      ∑                                          i                      =                      1                                        n                                    ⁢                                      xe2x80x83                                    ⁢                                                            (                                                                        Y                          i                                                -                                                  Y                          _                                                                    )                                        2                                                                                                          (        7        )                                D        =                              S            E                                              ∑                              i                =                1                            n                        ⁢                          xe2x80x83                        ⁢                                          (                                  a                  +                                      bX                    i                                                  )                            2                                                          (        8        )            
where the regression formula is expressed as Y=a+bX, Xi (i=1 to n) is the data for the criterion variable xe2x80x9cXxe2x80x9d of the regression formula, Yi (i=1 to n) is the data for the dependent variable xe2x80x9cYxe2x80x9d of the regression formula, {overscore (X)} is the mean value of Xi, and {overscore (Y)} is the mean value of Yi.
Further, according to the method of polarimetry, when a specimen to be detected is a urine, it is possible to provide a method of urinalysis for efficiently detecting the concentration of the spontaneous optical active substance in the urine.